The reptiles are a group of vertebrate animals. All reptiles
are tetrapods, they are all amniotes (animals whose embryos are surrounded
by an amniotic membrane). Today they are represented with four orders:

Order Crocodilia (crocodiles and alligators): 23 species
Order Rhynchocephalia (tuataras from New Zealand): 2 species
Order Squamata (lizards and snakes): approximately 7,600 species
Order Testudines (turtles): approximately 300 species

Reptiles are found on all continents except for Antarctica, although
their main distribution comprises the tropics and subtropics. Reptiles
don't have a constant body temperature. They are only able to a limited
extent to actively regulate their body temperature, which is largely dependent
on the environmental temperature. Most reptile species are carnivorous
and oviparous (egg-laying). Some species are ovoviviparous, and a few
species are truly viviparous.

However, note the below described taxonomy issues; mammals and birds
are all descendants of reptiles.

Classification of reptiles

Reptiles classically included all the amniotes except birds and mammals.
Thus reptiles were defined as the set of animals that includes crocodiles,
alligators, tuataras, lizards, snakes, and turtles, grouped together as
the class Reptilia. This is still the usual definition of the term.

However, in recent years many taxonomists have begun to insist that taxa
should be monophyletic, that is, groups should include all descendants
of a particular form. The reptiles as defined above would be paraphyletic,
since they exclude both birds and mammals, although these also developed
from the original reptile. Colin Tudge writes:

Mammals are a clade, and therefore the cladists are happy to
acknowledge the traditional taxon Mammalia; and birds, too, are a
clade, universally ascribed to the formal taxon Aves. Mammalia and
Aves are, in fact, subclades within the grand clade of the Amniota.
But the traditional class reptila is not a clade. It is just a section
of the clade Amniota: the section that is left after the Mammalia
and Aves have been hived off. It cannot be defined by synamorphies,
as is the proper way. It is instead defined by a combination of the
features it has and the features it lacks: reptiles are the amniotes
that lack fur or feathers. At best, the cladists suggest, we could
say that the traditional Reptila are 'non-avian, non-mammalian amniotes'.
(Tudge, p.85)

Some cladists thus redefine Reptilia as a monophyletic group, including
both the classic reptiles as well as the birds and perhaps the mammals
(depending on ideas about their relationships). Others abandon it as a
formal taxon altogether, dividing it into several different classes. However,
other biologists believe that the common characters of the standard four
orders are more important than the exact relationships, or feel that redefining
the Reptilia to include birds and mammals would be a confusing break with
tradition. A number of biologists have adopted a compromise system, marking
paraphyletic groups with an asterisk, e.g. class Reptilia*. Colin Tudge
notes other uses of this compromise system:

By the same token, the traditional clas Amphibia becomes Amphibia*,
because some ancient amphibian or other gave rise to all the amniotes;
and the phylum Crustecea becomes Crustacea*, because it may have given
rise to the insects and myriapods (centipedes and millipedes.) if
we believe, as some (but not all) zoologists do, that myripaods gave
rise to insects, then they should be called Myriapoda*....by this
convention Reptilla without an asterisk is synonmous with Amniota,
and incliudes birds and mammals, where as Reptila* means non-avian,
non-mammalian amniotes. (Tudge, p.85)